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  body: '{"contents":[{"parts":[{"text":"A train leaves Station A at 60 km/h. Another train leaves Station B (300 km away) 30 minutes later at 90 km/h heading toward Station A. At what time do they meet, and how far from Station A? Show your work.","thought":false}],"role":"user"}],"generationConfig":{"thinkingConfig":{"includeThoughts":true,"thinkingBudget":2048}},"safetySettings":null,"systemInstruction":{"parts":[{"text":"You are a helpful math tutor. Be concise.","thought":false}],"role":"model"},"toolConfig":null}'
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  - name: content-type
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  body: "data: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Defining the Parameters**\\n\\nI'm now zeroing in on defining the key variables for this relative motion problem. I've got to ensure the formulas cover the speeds, distances, and times of each train. I am also working on accounting for their relative motions. The goal is to arrive at the time of their meeting and the distance from Station A.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":67,\"totalTokenCount\":139}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Formulating the Equations**\\n\\nI've crafted equations to model the train problem now. I'm focusing on the relationship between time and distance, particularly how the head start impacts the calculations. The equations now incorporate the speeds of the trains, the total distance, and time variables for each. My next step is to solve for the time variable.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":461,\"totalTokenCount\":533}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Calculating the Meeting Time**\\n\\nI've just finished calculating the meeting time and distances. I now have the time each train travels until the meeting point, accounting for the 30-minute head start of the first train. The verification confirms the total distance traveled is correct. My next step involves defining the meeting time from the first train's departure. I need to consider whether to provide an elapsed time or a specific clock time, and I'm leaning toward elapsed time since no specific departure time is given.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":950,\"totalTokenCount\":1022}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Calculating the Meeting Distance**\\n\\nI've determined the meeting time as 2.3 hours after Train A's departure. Train A travels 138 km, confirming the meeting distance is 138 km from Station A. I feel I have a clear and consistent answer for both questions. I will verify if I can define a start time without ambiguity.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1245,\"totalTokenCount\":1317}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Refining the Solution**\\n\\nI've decided to express the meeting time as 2.3 hours after Train A's departure, or 1.8 hours after Train B's departure. This clarifies the \\\"At what time\\\" question. I've also re-verified the distance calculation and confirmed the meeting distance is 138 km from Station A. I think my solution is now complete and logically consistent, based on the problem.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1638,\"totalTokenCount\":1710}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Refining the Answer**\\n\\nI've finalized my response, opting for an elapsed time format for the meeting time due to the lack of a defined start time. The meeting occurs 2.3 hours after Train A departs, or 1.8 hours after Train B, with the meeting point at 138 km from Station A. This solution is clear and consistent.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1984,\"totalTokenCount\":2056}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Refining the Approach**\\n\\nI've decided to refine the answer with a focus on clarity. I'm choosing an approach where I define variables, account for the head start, use relative speed, and then calculate time and distance. I've re-verified and confirmed all the calculations, and I'm confident in the solution. I'm focusing on clearly articulating the final answer and how I've defined the departure time to avoid ambiguity.\\n\\nI've now finalized my calculations, and I'm ready to present a concise and clear answer.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":2044,\"totalTokenCount\":2116}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"Here's how to solve the problem:\\n\\n1.  **Train A's head start:**\\n    Train A travels for 30 minutes (0.5 hours) before\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"candidatesTokenCount\":31,\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":2044,\"totalTokenCount\":2147}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" Train B leaves.\\n    Distance covered by Train A: $60 \\\\text{ km/h} \\\\times 0.5 \\\\text{ h} = 30 \\\\text{ km}$.\\n\\n2.  **Remaining\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"candidatesTokenCount\":79,\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":2044,\"totalTokenCount\":2195}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" distance:**\\n    When Train B leaves, the distance between the trains is $300 \\\\text{ km} - 30 \\\\text{ km} = 270 \\\\text{ km}$.\\n\\n3.  **Relative speed\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"candidatesTokenCount\":129,\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":2044,\"totalTokenCount\":2245}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\":**\\n    Since the trains are moving towards each other, their speeds add up.\\n    Relative speed: $60 \\\\text{ km/h} + 90 \\\\text{ km/h} = 150 \\\\text\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"candidatesTokenCount\":179,\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":2044,\"totalTokenCount\":2295}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"{ km/h}$.\\n\\n4.  **Time to meet (after Train B leaves):**\\n    Time = Distance / Speed\\n    Time to meet: $270 \\\\text{ km} / 150 \\\\text{\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"candidatesTokenCount\":229,\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":2044,\"totalTokenCount\":2345}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" km/h} = 1.8 \\\\text{ hours}$.\\n\\n5.  **Total time elapsed from Train A's departure:**\\n    Total time = Head start time + Time to meet\\n    Total time: $0.5\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"candidatesTokenCount\":279,\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":2044,\"totalTokenCount\":2395}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" \\\\text{ hours} + 1.8 \\\\text{ hours} = 2.3 \\\\text{ hours}$.\\n\\n6.  **Distance from Station A:**\\n    Distance = Speed of Train A $\\\\times$ Total time\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"candidatesTokenCount\":327,\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":2044,\"totalTokenCount\":2443}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" Train A traveled\\n    Distance from Station A: $60 \\\\text{ km/h} \\\\times 2.3 \\\\text{ h} = 138 \\\\text{ km}$.\\n\\nSince no specific departure time for Train A\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"candidatesTokenCount\":377,\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":2044,\"totalTokenCount\":2493}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" was given, we state the time elapsed.\\n\\n**Answer:**\\n*   They meet **2.3 hours** after Train A leaves (or 1.8 hours after Train B leaves).\\n*   They meet **138\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"candidatesTokenCount\":426,\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":2044,\"totalTokenCount\":2542}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" km** from Station A.\"}],\"role\":\"model\"},\"finishReason\":\"STOP\",\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_1\",\"usageMetadata\":{\"candidatesTokenCount\":432,\"promptTokenCount\":72,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":72}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":2044,\"totalTokenCount\":2548}}\r\n\r\n"
---
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  body: '{"contents":[{"parts":[{"text":"A train leaves Station A at 60 km/h. Another train leaves Station B (300 km away) 30 minutes later at 90 km/h heading toward Station A. At what time do they meet, and how far from Station A? Show your work.","thought":false}],"role":"user"},{"parts":[{"text":"**Defining the Parameters**\n\nI''m now zeroing in on defining the key variables for this relative motion problem. I''ve got to ensure the formulas cover the speeds, distances, and times of each train. I am also working on accounting for their relative motions. The goal is to arrive at the time of their meeting and the distance from Station A.\n\n\n**Formulating the Equations**\n\nI''ve crafted equations to model the train problem now. I''m focusing on the relationship between time and distance, particularly how the head start impacts the calculations. The equations now incorporate the speeds of the trains, the total distance, and time variables for each. My next step is to solve for the time variable.\n\n\n**Calculating the Meeting Time**\n\nI''ve just finished calculating the meeting time and distances. I now have the time each train travels until the meeting point, accounting for the 30-minute head start of the first train. The verification confirms the total distance traveled is correct. My next step involves defining the meeting time from the first train''s departure. I need to consider whether to provide an elapsed time or a specific clock time, and I''m leaning toward elapsed time since no specific departure time is given.\n\n\n**Calculating the Meeting Distance**\n\nI''ve determined the meeting time as 2.3 hours after Train A''s departure. Train A travels 138 km, confirming the meeting distance is 138 km from Station A. I feel I have a clear and consistent answer for both questions. I will verify if I can define a start time without ambiguity.\n\n\n**Refining the Solution**\n\nI''ve decided to express the meeting time as 2.3 hours after Train A''s departure, or 1.8 hours after Train B''s departure. This clarifies the \"At what time\" question. I''ve also re-verified the distance calculation and confirmed the meeting distance is 138 km from Station A. I think my solution is now complete and logically consistent, based on the problem.\n\n\n**Refining the Answer**\n\nI''ve finalized my response, opting for an elapsed time format for the meeting time due to the lack of a defined start time. The meeting occurs 2.3 hours after Train A departs, or 1.8 hours after Train B, with the meeting point at 138 km from Station A. This solution is clear and consistent.\n\n\n**Refining the Approach**\n\nI''ve decided to refine the answer with a focus on clarity. I''m choosing an approach where I define variables, account for the head start, use relative speed, and then calculate time and distance. I''ve re-verified and confirmed all the calculations, and I''m confident in the solution. I''m focusing on clearly articulating the final answer and how I''ve defined the departure time to avoid ambiguity.\n\nI''ve now finalized my calculations, and I''m ready to present a concise and clear answer.\n\n\n","thought":true},{"text":"Here''s how to solve the problem:\n\n1.  **Train A''s head start:**\n    Train A travels for 30 minutes (0.5 hours) before Train B leaves.\n    Distance covered by Train A: $60 \\text{ km/h} \\times 0.5 \\text{ h} = 30 \\text{ km}$.\n\n2.  **Remaining distance:**\n    When Train B leaves, the distance between the trains is $300 \\text{ km} - 30 \\text{ km} = 270 \\text{ km}$.\n\n3.  **Relative speed:**\n    Since the trains are moving towards each other, their speeds add up.\n    Relative speed: $60 \\text{ km/h} + 90 \\text{ km/h} = 150 \\text{ km/h}$.\n\n4.  **Time to meet (after Train B leaves):**\n    Time = Distance / Speed\n    Time to meet: $270 \\text{ km} / 150 \\text{ km/h} = 1.8 \\text{ hours}$.\n\n5.  **Total time elapsed from Train A''s departure:**\n    Total time = Head start time + Time to meet\n    Total time: $0.5 \\text{ hours} + 1.8 \\text{ hours} = 2.3 \\text{ hours}$.\n\n6.  **Distance from Station A:**\n    Distance = Speed of Train A $\\times$ Total time Train A traveled\n    Distance from Station A: $60 \\text{ km/h} \\times 2.3 \\text{ h} = 138 \\text{ km}$.\n\nSince no specific departure time for Train A was given, we state the time elapsed.\n\n**Answer:**\n*   They meet **2.3 hours** after Train A leaves (or 1.8 hours after Train B leaves).\n*   They meet **138 km** from Station A.","thought":false}],"role":"model"},{"parts":[{"text":"Now suppose both trains slow down by 10 km/h after traveling half the original distance. When do they meet now?","thought":false}],"role":"user"}],"generationConfig":{"thinkingConfig":{"includeThoughts":true,"thinkingBudget":2048}},"safetySettings":null,"systemInstruction":{"parts":[{"text":"You are a helpful math tutor. Be concise.","thought":false}],"role":"model"},"toolConfig":null}'
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  body: "data: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Adjusting the Parameters**\\n\\nI'm now adapting the model. The core shift is a speed reduction of 10 km/h for both trains, but this happens *after* they've each covered half the initial distance (150 km). I'm refining the problem definition to incorporate this new condition.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":67,\"totalTokenCount\":1224}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Refining the Scenario**\\n\\nI'm now detailing the scenario's phases. Phase one involves calculating Train A's head start distance (30km). This reduces the effective separation to 270 km when Train B starts. The critical step is recognizing both trains slow down *after* each covers 150 km, which I am now carefully incorporating into the model.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":412,\"totalTokenCount\":1569}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Clarifying the Ambiguity**\\n\\nI'm now clarifying the ambiguity around the point of speed reduction. I've decided that each train's speed change occurs *independently* after they have each individually covered half the total distance (150 km) from their respective starting points, as this is the most natural interpretation of the statement. I am modelling each train's state for each phase independently.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":714,\"totalTokenCount\":1871}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Modeling the Slowdown**\\n\\nI'm now precisely modeling the speed reduction. I've broken the scenario into phases. I'm focusing on the condition that each train slows down after traveling half the original distance (150 km). I'm carefully analyzing the meeting point and the timing of each train's speed reduction based on this condition. I am now incorporating these conditions into my formal model.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1059,\"totalTokenCount\":2216}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"**Modeling the Meeting**\\n\\nI am now structuring the problem into two distinct phases to account for the speed reductions. I've calculated that Train A covers the first 120 km (beyond its head start) in two hours, while Train B covers 150 km. I'm focusing on precisely timing the trains' slowdowns, and then calculating where they meet.\\n\\n\\n\",\"thought\":true}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2268}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"This problem requires breaking it into phases because the speeds change mid-journey. \\\"Half the original distance\\\" refers to 150 km from each train's starting station.\\n\\n**Initial Setup:**\\n*   Train A speed\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":42,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2310}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\": $V_A = 60 \\\\text{ km/h}$\\n*   Train B speed: $V_B = 90 \\\\text{ km/h}$\\n*   Total distance: $D = 30\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":92,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2360}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"0 \\\\text{ km}$\\n*   Train A head start: $t_{head} = 30 \\\\text{ min} = 0.5 \\\\text{ h}$\\n\\n**Phase 1: Train A's head\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":141,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2409}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" start**\\n*   Distance covered by Train A: $d_{A,head} = V_A \\\\times t_{head} = 60 \\\\text{ km/h} \\\\times 0.5 \\\\text{\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":189,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2457}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" h} = 30 \\\\text{ km}$.\\n*   When Train B leaves, Train A is 30 km from Station A.\\n*   Remaining distance between trains: $D_1 = 300 \\\\text{ km\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":240,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2508}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"} - 30 \\\\text{ km} = 270 \\\\text{ km}$.\\n\\n**Phase 2: Travel until one train reaches its 150 km mark**\\nBoth trains slow down after covering 15\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":289,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2557}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"0 km *from their respective starting points*.\\n\\n*   Train A needs to cover $150 \\\\text{ km} - 30 \\\\text{ km} = 120 \\\\text{ km}$ more at $\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":337,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2605}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"V_A$ before slowing down.\\n    Time for Train A to reach 150 km mark (after Train B starts): $t_{A,slow} = 120 \\\\text{ km} / 60\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":386,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2654}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" \\\\text{ km/h} = 2 \\\\text{ hours}$.\\n*   Train B needs to cover $150 \\\\text{ km}$ at $V_B$ before slowing down.\\n    Time for Train B\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":434,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2702}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" to reach 150 km mark (after Train B starts): $t_{B,slow} = 150 \\\\text{ km} / 90 \\\\text{ km/h} = 1.66\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":482,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2750}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"6... \\\\text{ hours}$.\\n\\nSince $t_{B,slow} < t_{A,slow}$, Train B will be the first to reach its 150 km mark and slow down.\\n\\nLet's calculate what\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":530,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2798}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" happens during $t_{B,slow} = 1.666... \\\\text{ hours}$ after Train B leaves:\\n*   Distance covered by Train B: $d_{B,P2} = 90 \\\\text\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":581,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2849}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"{ km/h} \\\\times (5/3) \\\\text{ h} = 150 \\\\text{ km}$.\\n*   Distance covered by Train A: $d_{A,P2} = 60 \\\\\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":630,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2898}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"text{ km/h} \\\\times (5/3) \\\\text{ h} = 100 \\\\text{ km}$.\\n*   Train A's position from Station A: $30 \\\\text{ km}\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":678,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2946}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" (\\\\text{head start}) + 100 \\\\text{ km} = 130 \\\\text{ km}$.\\n*   Train B's position from Station B: $150 \\\\text{ km}$.\\n\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":725,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":2993}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"*   Distance remaining between them: $300 \\\\text{ km} - 130 \\\\text{ km} (\\\\text{from A}) - 150 \\\\text{ km} (\\\\text{from B})\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":773,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":3041}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" = 20 \\\\text{ km}$.\\n\\n**Phase 3: The final stretch (both speeds might change or one has already changed)**\\n\\nAt this point (1.666... hours after Train B left):\\n*   \"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":821,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":3089}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"Train B has reached its 150 km mark and slows down to $V'_B = 90 - 10 = 80 \\\\text{ km/h}$.\\n*   Train A is at 13\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":869,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":3137}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"0 km from Station A, so it has NOT yet reached its 150 km mark. Its speed is still $V_A = 60 \\\\text{ km/h}$.\\n*   The distance between them is 20 km\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":920,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":3188}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\".\\n\\nThey are now traveling towards each other with different speeds.\\n*   Relative speed: $V_A + V'_B = 60 \\\\text{ km/h} + 80 \\\\text{ km/h} =\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":970,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":3238}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" 140 \\\\text{ km/h}$.\\n*   Time to meet in this phase: $t_{meet,P3} = 20 \\\\text{ km} / 140 \\\\text{ km/h\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":1018,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":3286}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"} = 1/7 \\\\text{ hours}$.\\n\\n**Total time until they meet (from when Train A left):**\\n\\nTotal time = Train A's head start + Time in Phase 2 + Time in Phase 3\\n\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":1066,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":3334}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"Total time = $0.5 \\\\text{ h} + (5/3) \\\\text{ h} + (1/7) \\\\text{ h}$\\nTotal time $\\\\approx 0.5 + 1.666\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":1116,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":3384}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"7 + 0.1429 \\\\approx 2.3096 \\\\text{ hours}$.\\n\\nTo express this more precisely:\\nTotal time = $1/2 + 5/3 + 1/7\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":1164,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":3432}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\" = (21 + 70 + 6) / 42 = 97/42 \\\\text{ hours}$.\\n\\n**Answer:**\\nThey meet **97/42 hours** (approximately 2.\"}],\"role\":\"model\"},\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":1212,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":3480}}\r\n\r\ndata: {\"candidates\":[{\"content\":{\"parts\":[{\"text\":\"31 hours) after Train A leaves.\"}],\"role\":\"model\"},\"finishReason\":\"STOP\",\"index\":0}],\"modelVersion\":\"gemini-2.5-flash\",\"responseId\":\"id_REDACTED_2\",\"usageMetadata\":{\"candidatesTokenCount\":1221,\"promptTokenCount\":1157,\"promptTokensDetails\":[{\"modality\":\"TEXT\",\"tokenCount\":1157}],\"serviceTier\":\"standard\",\"thoughtsTokenCount\":1111,\"totalTokenCount\":3489}}\r\n\r\n"
